Q. ab+bc+ca=0 find value 1/(b2-ac ) + 1/(c2-ab) + 1/(a2-bc)Solution: ab+bc+ca=0 find value 1/(a2-bc ) + 1/(c2-ab) + 1/(a2-bc) Put -ac = ab + bc ; -ab = ac+ bc and -bc =ab + ac you get : 1/(a2-bc (ab + bc + ca)/[(a+b+c)(abc)] put, ab+bc+ca=0 you get value = 0/[(a+b+c)(abc)] = 0 Q. A class of 20 boys and 15 girls is divided into n groups so that each group has x boys and y girls. Find x ,y and n.
Sol: n(x+y) = 20 + 15 = 35 Total boys = nx = 20 Þ nx = 2 x 10 = 4 x 5 = 10 x 2 Similarly, Total girls = ny = 15 Þ 3 x 5 The possible value of n may be n = 5 x = 4 and y = 5 OR, Hcf of 20 and 15 is 5 Þ No. of group will be n =5 then Total girls = ny = 15 Þ 3 x 5 The possible value of n may be n = 5 x = 4 and y = 5 Q. The pair of equations y=0 and y= -5 has 1.one solution 2.two solutions 3.infinitely many solutions 4.no solution Ans: o.x + y = 0 0.x + y = -5 therefore, a1/a2 = b1/b2 ≠ c1/c2 Þ The pair of equations y=0 and y= -5 has no solution Q. If secA + tanA = 1/x find the value of SecA and tanA Q. There are 20 cars and motorcycle in a parking lot. If there are 56 wheels together find the no of cars and motorcycles Ans: Le t the no. of car is x then no. of motorcycle will be (20-x) A/Q, 4x + 2(20-x) = 56 Þ x = 8 the no. of car is x = 8 then no. of motorcycle will be (20-x) = 20-8 = 12 Q. If constant term in Quardatic polynomial is zero ,then prove that one of its zero is zero Sol: let the quadratic polynomial be P(x) = a x2 + bx + c Þ P(x) = a x2 + bx [since the constant term is zero] Now P(0) = 0 + 0 = 0 Thus, 0 is one zero of p(x). Q. If p(x) = ax2 + bx +c and a + c = b, then one of the zeroes is (a) b/a (b) c/a (c) -c/a (d) -b/a Sol: c/a Q. if asin2q + bcos2 q = c , then sow that cot2q = (c-a)/(b-c) ab + ac ab + ac (ab + bc + ca)/[(a+b+c)(abc)] put, ab+bc+ca=0 you get value = 0/[(a+b+c)(abc)] = 0 Q. A class of 20 boys and 15 girls is divided into n groups so that each group has x boys and y girls. Find x ,y and n. Sol: n(x+y) = 20 + 15 = 35 Total boys = nx = 20 Þ nx = 2 x 10 = 4 x 5 = 10 x 2 Similarly, Total girls = ny = 15 Þ 3 x 5 The possible value of n may be n = 5 x = 4 and y = 5 OR, Hcf of 20 and 15 is 5 Þ No. of group will be n =5 then Total girls = ny = 15 Þ 3 x 5 The possible value of n may be n = 5 x = 4 and y = 5 Q. The pair of equations y=0 and y= -5 has 1.one solution 2.two solutions 3.infinitely many solutions 4.no solution Ans: o.x + y = 0 0.x + y = -5 therefore, a1/a2 = b1/b2 ≠ c1/c2 Þ The pair of equations y=0 and y= -5 has no solution Q. If secA + tanA = 1/x find the value of SecA and tanA Q. There are 20 cars and motorcycle in a parking lot. If there are 56 wheels together find the no of cars and motorcycles Ans: Le t the no. of car is x then no. of motorcycle will be (20-x) A/Q, 4x + 2(20-x) = 56 Þ x = 8 the no. of car is x = 8 then no. of motorcycle will be (20-x) = 20-8 = 12 Q. If constant term in Quardatic polynomial is zero ,then prove that one of its zero is zero Sol: let the quadratic polynomial be P(x) = a x2 + bx + c Þ P(x) = a x2 + bx [since the constant term is zero] Now P(0) = 0 + 0 = 0 Thus, 0 is one zero of p(x). Q. If p(x) = ax2 + bx +c and a + c = b, then one of the zeroes is (a) b/a (b) c/a (c) -c/a (d) -b/a Sol: c/a Q. if asin2q + bcos2 q = c , then sow that cot2q = (c-a)/(b-c)
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Contents: 1. Thrust and Pressure 2. Pressure in Fluids 3. Buoyancy 4. Why objects sink or Float when placed on surface of water? 5. Archimedes Principle 6. Relative Density Learning Objectives: The students will: 1. Understand the difference between Thrust and Pressure. 2. Apply Pressure to daily life. 3. Explain Pressure in fluids. 4. Understand Buoyancy. 5. Understand and explain Archimedes Principle. 6. Applies Archimedes Principle on floating objects. 7. Understand relation between Density of a Solid and Density of a Liquid. Key Terms : 1. Thrust 2. Pressure 3. Pascal 4. Buoyancy 5. Archimedes Principle 6. Relative Density LIST OF PRACTICALS 1. To determine the density of a solid (denser than water) by using spring balance and a measuring cylinder. 2. To establish the relation between loss in weight of a solid when fully immersed in (i) tap water (ii) strongly salty water, with weight of water displaced by it taking at least two different solids. 3. To Calculate the pressure exerted by a wooden block on sand. Download full Study Note for BOARD EXAM [Given below]
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